Syracuse trails the best-of-7 series 3-2 with Game 6 at Grand Rapids on Tuesday.
Syracuse, the American Hockey League affiliate of the Tampa Bay Lightning, scored 17 seconds into the period and with 44 seconds remaining.
Kevin Lynch gave Syracuse a 1-0 lead, which was followed by goals from Mathieu Brodeur (4:33), Byron Froese (14:05), Cory Conacher (17:19) and Ben Thomas. Yanni Gourde had three assists.
Ben Street scored for Grand Rapids, the affiliate of the Detroit Red Wings, 5:58 into the third period.
Mike McKenna made 36 saves for Syracuse. Eddie Pasquale saved all 19 shots he faced for Grand Rapids in relief of Jared Coreau, who allowed five goals on 12 shots.
